Question

the difference between two numbers is 3 the sum of thrice the larger number and twice smaller number is 19. then find the number​

Answer 1

$\Large {\underline { \sf \orange{Clarification :}}}$

Here, we are given that the the difference between two numbers is 3 and the sum of thrice the larger number and twice smaller number is 19. We have to find out two numbers.

We'll assume the numbers as variables, say x and y ; as they are unknown. After that, as per the given question we'll form two algebraic equations in two variables. As there are two variables, so by using substitution method we'll find the larger number and the smaller number.

$\Large {\underline { \sf \orange{Explication \: of \: Steps :}}}$

Let,

• Larger number = x
• Smaller number = y

According to the question ,

$\underline{ \underline{ \sf{Equation \; \frak{(1) :}}}}$

$\longrightarrow \sf { Difference_{(Two \: Numbers)} = 3 }$

$\longrightarrow \sf { x - y = 3 }$

From this equation,

$\longrightarrow \bf { x = 3 + y }$

$\underline{ \underline{ \sf{Equation \; \frak{(2) :}}}}$

$\longrightarrow \sf { 3(Number_{(Larger)}) + 2(Number_{(Smaller)}) = 19 }$

$\longrightarrow \bf { 3x + 2y = 19 }$

We'll work on this equation to find the value of y. Substitute the value of x from the first equation.

$\longrightarrow \sf { 3(3+y) + 2y = 19 }$

$\longrightarrow \sf { 3(3) + 3(y) + 2y = 19 }$

$\longrightarrow \sf { 9 + 3y + 2y = 19 }$

$\longrightarrow \sf { 9 + 5y = 19 }$

$\longrightarrow \sf { 5y = 19 -9 }$

$\longrightarrow \sf { 5y = 10 }$

$\longrightarrow \sf { y = \cancel { \dfrac{10}{5}} }$

$\longrightarrow \boxed{\sf { y = 2 } }$

Also, from the first equation,

$\longrightarrow \bf { x = 3 + y }$

Substituting the value of y to find the value of x.

$\longrightarrow \sf { x = 3 + 2 }$

$\longrightarrow \boxed{ \sf { x = 5 } }$

Therefore,

$\longrightarrow \underline{\boxed{\sf{ x_{(Larger \: Number)} = 5 }}} \: \orange{\bigstar}$

$\longrightarrow \underline{\boxed{\sf{ y_{(Smaller \: Number)} = 3 }}} \: \orange{\bigstar}$